<?xml version="1.0"?>
<div class="add">

<span class="kw">let </span><font color="Maroon" title="c1">k</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="ami_2.html#K5" title="AMI_2:func.5">NAT</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">s</font> being  <a href="ami_1.html#NM5" title="AMI_1:NM.5">State</a> of <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a>  holds   <a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p1">(<span class="default"><a href="reloc.html#K1" title="RELOC:func.1">IncAddr</a> <span class="p2">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Olive" title="b1">s</font></span>)</span>,<font color="Olive" title="b1">s</font></span>)</span>,<font color="Maroon" title="c1">k</font></span>)</span>,<span class="p1">(<span class="default"><font color="Olive" title="b1">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Olive" title="b1">s</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c1">k</font></span>)</span>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Following</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Olive" title="b1">s</font></span>)</span>,<font color="Olive" title="b1">s</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p4">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Following</a> <span class="p5">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Olive" title="b1">s</font></span>)</span>,<font color="Olive" title="b1">s</font></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c1">k</font></span>)</span>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c2">s</font> be   <a href="ami_1.html#NM5" title="AMI_1:NM.5">State</a> of <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  <a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p1">(<span class="default"><a href="reloc.html#K1" title="RELOC:func.1">IncAddr</a> <span class="p2">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c1">k</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c2">s</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c1">k</font></span>)</span>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Following</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p4">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Following</a> <span class="p5">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c1">k</font></span>)</span>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span><br/>



<span class="kw">set </span><font color="Maroon" title="c3">INS</font> =  <a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c4">m</font> =  <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c2">s</font> as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="ami_2.html#K5" title="AMI_2:func.5">NAT</a>  ;<br/>
<span class="lab"><font color="Green" title="E25">A1</font></span>:  <a href="scmnorm.html#K1" title="SCMNORM:func.1">succ</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c2">s</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c1">k</font></span>)</span>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span>)</span></span>)</span> = 
 <a href="scmnorm.html#K1" title="SCMNORM:func.1">succ</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c1">k</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_4.html#T121" title="FUNCT_4:th.121">FUNCT_4:121</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c4">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c1">k</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1
<span class="kw">by</span> <span class="lab"><a class="ref" href="nat_1.html#T39" title="NAT_1:th.39">NAT_1:39</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c4">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c1">k</font>

<br/>.= 
<span class="p1">(<span class="default"><a href="scmnorm.html#K1" title="SCMNORM:func.1">succ</a> <span class="p2">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c2">s</font></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c1">k</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="nat_1.html#T39" title="NAT_1:th.39">NAT_1:39</a></span>
<br/>.= 
 <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p3">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p4">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmnorm.html#K1" title="SCMNORM:func.1">succ</a> <span class="p5">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c2">s</font></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c1">k</font></span>)</span>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_4.html#T121" title="FUNCT_4:th.121">FUNCT_4:121</a></span>
;<br/>
<div><span class="lab"><font color="Green" title="E26">A2</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="35_2"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c5">d</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="ami_2.html#K5" title="AMI_2:func.5">NAT</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c2">s</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c1">k</font></span>)</span>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K12" title="AMI_1:func.12">.</a> <font color="Maroon" title="c5">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p3">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p4">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmnorm.html#K1" title="SCMNORM:func.1">succ</a> <span class="p5">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c2">s</font></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c1">k</font></span>)</span>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span>)</span> <a href="ami_1.html#K12" title="AMI_1:func.12">.</a> <font color="Maroon" title="c5">d</font></span><br/><span class="kw">thus </span><span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c2">s</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c1">k</font></span>)</span>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K12" title="AMI_1:func.12">.</a> <font color="Maroon" title="c5">d</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c2">s</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c1">k</font></span>)</span>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span>)</span> <a href="ami_1.html#K12" title="AMI_1:func.12">.</a> <font color="Maroon" title="c5">d</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="ami_1.html#D13" title="AMI_1:def.13">AMI_1:def 13</a></span>
<br/>.= 
<font color="Maroon" title="c2">s</font> <a href="ami_1.html#K12" title="AMI_1:func.12">.</a> <font color="Maroon" title="c5">d</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="ami_1.html#T112" title="AMI_1:th.112">AMI_1:112</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span> <a href="ami_1.html#K12" title="AMI_1:func.12">.</a> <font color="Maroon" title="c5">d</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="ami_1.html#D13" title="AMI_1:def.13">AMI_1:def 13</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p3">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p4">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmnorm.html#K1" title="SCMNORM:func.1">succ</a> <span class="p5">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c2">s</font></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c1">k</font></span>)</span>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span>)</span> <a href="ami_1.html#K12" title="AMI_1:func.12">.</a> <font color="Maroon" title="c5">d</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="ami_1.html#T112" title="AMI_1:th.112">AMI_1:112</a></span>
; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="35_3"><span class="kw">per </span></a><a class="txt" onclick="hs(this)" href="javascript:()"><span class="kw">cases </span></a><span class="hide"><a NAME="E1:35_3"/>
(  <a href="ami_1.html#K21" title="AMI_1:func.21">InsCode</a> <span class="p1">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  or  <a href="ami_1.html#K21" title="AMI_1:func.21">InsCode</a> <span class="p1">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 or  <a href="ami_1.html#K21" title="AMI_1:func.21">InsCode</a> <span class="p1">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2 or  <a href="ami_1.html#K21" title="AMI_1:func.21">InsCode</a> <span class="p1">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 3 or  <a href="ami_1.html#K21" title="AMI_1:func.21">InsCode</a> <span class="p1">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 4 or  <a href="ami_1.html#K21" title="AMI_1:func.21">InsCode</a> <span class="p1">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 5 or  <a href="ami_1.html#K21" title="AMI_1:func.21">InsCode</a> <span class="p1">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 6 or  <a href="ami_1.html#K21" title="AMI_1:func.21">InsCode</a> <span class="p1">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 7 or  <a href="ami_1.html#K21" title="AMI_1:func.21">InsCode</a> <span class="p1">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 8 )
 </span><span class="kw">by</span> <span class="lab"><a class="ref" href="ami_5.html#T36" title="AMI_5:th.36">AMI_5:36</a>, <a class="ref" href="nat_1.html#T33" title="NAT_1:th.33">NAT_1:33</a></span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="35_3_1"><span class="kw">suppose </span></a><a NAME="E1:35_3_1"/>
 <a href="ami_1.html#K21" title="AMI_1:func.21">InsCode</a> <span class="p1">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  <a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p1">(<span class="default"><a href="reloc.html#K1" title="RELOC:func.1">IncAddr</a> <span class="p2">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c1">k</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c2">s</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c1">k</font></span>)</span>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Following</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p4">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Following</a> <span class="p5">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c1">k</font></span>)</span>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span><br/><div class="add"><a NAME="E2:35_3_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E27">A3</font></span>: 
 <a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K5" title="AMI_1:func.5">halt</a> <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="ami_5.html#T46" title="AMI_5:th.46">AMI_5:46</a></span>;<br/><a NAME="E3:35_3_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E28">A4</font></span>: 
 <a href="ami_1.html#K9" title="AMI_1:func.9">Following</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">s</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="ami_1.html#D8" title="AMI_1:def.8">AMI_1:def 8</a></span>;<br/><span class="kw">thus </span> <a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p1">(<span class="default"><a href="reloc.html#K1" title="RELOC:func.1">IncAddr</a> <span class="p2">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c1">k</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c2">s</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c1">k</font></span>)</span>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span>)</span> = 
 <a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p1">(<span class="default"><a href="ami_1.html#K5" title="AMI_1:func.5">halt</a> <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c2">s</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c1">k</font></span>)</span>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:35_3_1"><span class="lab"><font color="Green" title="E27">A3</font></span></a>, <a class="ref" href="reloc.html#D3" target="_self" title="RELOC:def.3">Def3</a>, <a class="ref" href="ami_5.html#T37" title="AMI_5:th.37">AMI_5:37</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Following</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p4">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Following</a> <span class="p5">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c1">k</font></span>)</span>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:35_3_1"><span class="lab"><font color="Green" title="E28">A4</font></span></a>, <a class="ref" href="ami_1.html#D8" title="AMI_1:def.8">AMI_1:def 8</a></span>
; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="35_3_2"><span class="kw">suppose </span></a><a NAME="E1:35_3_2"/>
 <a href="ami_1.html#K21" title="AMI_1:func.21">InsCode</a> <span class="p1">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  <a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p1">(<span class="default"><a href="reloc.html#K1" title="RELOC:func.1">IncAddr</a> <span class="p2">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c1">k</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c2">s</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c1">k</font></span>)</span>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Following</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p4">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Following</a> <span class="p5">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c1">k</font></span>)</span>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span><br/><div class="add"><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c5">da</font>, <font color="Maroon" title="c6">db</font> being    <a href="ami_3.html#M1" title="AMI_3:mode.1">Data-Location</a> <span class="kw"> such that </span><br/><a NAME="E3:35_3_2"/><span class="lab"><font color="Green" title="E27">A5</font></span>: 
 <a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">da</font> <a href="ami_3.html#K3" title="AMI_3:func.3">:=</a> <font color="Maroon" title="c6">db</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="ami_5.html#T47" title="AMI_5:th.47">AMI_5:47</a></span>;<br/><div><span class="lab"><font color="Green" title="E28">A6</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="35_3_2_1"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c7">d</font> be    <a href="ami_3.html#M1" title="AMI_3:mode.1">Data-Location</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c2">s</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c1">k</font></span>)</span>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p3">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p4">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmnorm.html#K1" title="SCMNORM:func.1">succ</a> <span class="p5">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c2">s</font></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c1">k</font></span>)</span>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Olive">b<sub>1</sub></font></span><br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="35_3_2_1_1"><span class="kw">per </span></a><a class="txt" onclick="hs(this)" href="javascript:()"><span class="kw">cases </span></a><span class="hide"><a NAME="E1:35_3_2_1_1"/>
( <font color="Maroon" title="c5">da</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">d</font> or <font color="Maroon" title="c5">da</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c7">d</font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="35_3_2_1_1_1"><span class="kw">suppose </span></a><a NAME="E1:35_3_2_1_1_1"/><span class="lab"><font color="Green" title="E29">A7</font></span>: 
<font color="Maroon" title="c5">da</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">d</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c2">s</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c1">k</font></span>)</span>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p3">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p4">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmnorm.html#K1" title="SCMNORM:func.1">succ</a> <span class="p5">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c2">s</font></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c1">k</font></span>)</span>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Olive">b<sub>1</sub></font></span><br/><div class="add"><span class="kw">hence </span><span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c2">s</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c1">k</font></span>)</span>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c7">d</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c2">s</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c1">k</font></span>)</span>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c6">db</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:35_3_2"><span class="lab"><font color="Green" title="E27">A5</font></span></a>, <a class="ref" href="ami_3.html#T8" title="AMI_3:th.8">AMI_3:8</a></span>
<br/>.= 
<font color="Maroon" title="c2">s</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c6">db</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="ami_5.html#T80" title="AMI_5:th.80">AMI_5:80</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c7">d</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:35_3_2"><span class="lab"><font color="Green" title="E27">A5</font></span></a>, <a class="txt" href="#E1:35_3_2_1_1_1"><span class="lab"><font color="Green" title="E29">A7</font></span></a>, <a class="ref" href="ami_3.html#T8" title="AMI_3:th.8">AMI_3:8</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p3">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p4">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmnorm.html#K1" title="SCMNORM:func.1">succ</a> <span class="p5">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c2">s</font></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c1">k</font></span>)</span>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c7">d</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="ami_5.html#T80" title="AMI_5:th.80">AMI_5:80</a></span>
;<br/> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="35_3_2_1_1_2"><span class="kw">suppose </span></a><a NAME="E1:35_3_2_1_1_2"/><span class="lab"><font color="Green" title="E29">A8</font></span>: 
<font color="Maroon" title="c5">da</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c7">d</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c2">s</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c1">k</font></span>)</span>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p3">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p4">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmnorm.html#K1" title="SCMNORM:func.1">succ</a> <span class="p5">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c2">s</font></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c1">k</font></span>)</span>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Olive">b<sub>1</sub></font></span><br/><div class="add"><span class="kw">hence </span><span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c2">s</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c1">k</font></span>)</span>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c7">d</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c2">s</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c1">k</font></span>)</span>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c7">d</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:35_3_2"><span class="lab"><font color="Green" title="E27">A5</font></span></a>, <a class="ref" href="ami_3.html#T8" title="AMI_3:th.8">AMI_3:8</a></span>
<br/>.= 
<font color="Maroon" title="c2">s</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c7">d</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="ami_5.html#T80" title="AMI_5:th.80">AMI_5:80</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c7">d</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:35_3_2"><span class="lab"><font color="Green" title="E27">A5</font></span></a>, <a class="txt" href="#E1:35_3_2_1_1_2"><span class="lab"><font color="Green" title="E29">A8</font></span></a>, <a class="ref" href="ami_3.html#T8" title="AMI_3:th.8">AMI_3:8</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p3">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p4">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmnorm.html#K1" title="SCMNORM:func.1">succ</a> <span class="p5">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c2">s</font></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c1">k</font></span>)</span>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c7">d</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="ami_5.html#T80" title="AMI_5:th.80">AMI_5:80</a></span>
;<br/> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div><a NAME="E5:35_3_2"/><span class="lab"><font color="Green" title="E29">A9</font></span>: 
 <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c2">s</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c1">k</font></span>)</span>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p3">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p4">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmnorm.html#K1" title="SCMNORM:func.1">succ</a> <span class="p5">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c2">s</font></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c1">k</font></span>)</span>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:35"><span class="lab"><font color="Green" title="E25">A1</font></span></a>, <a class="txt" href="#E3:35_3_2"><span class="lab"><font color="Green" title="E27">A5</font></span></a>, <a class="ref" href="ami_3.html#T8" title="AMI_3:th.8">AMI_3:8</a></span>;<br/><a NAME="E6:35_3_2"/>
(  <a href="reloc.html#K1" title="RELOC:func.1">IncAddr</a> <span class="p1">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c1">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font> &amp;  <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmnorm.html#K1" title="SCMNORM:func.1">succ</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c2">s</font></span>)</span> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:35_3_2"><span class="lab"><font color="Green" title="E27">A5</font></span></a>, <a class="ref" href="reloc.html#T5" target="_self" title="RELOC:th.5">Th5</a>, <a class="ref" href="ami_3.html#T8" title="AMI_3:th.8">AMI_3:8</a></span>;<br/><span class="kw">hence </span><a NAME="E7:35_3_2"/>
 <a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p1">(<span class="default"><a href="reloc.html#K1" title="RELOC:func.1">IncAddr</a> <span class="p2">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c1">k</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c2">s</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c1">k</font></span>)</span>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Following</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p4">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Following</a> <span class="p5">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c1">k</font></span>)</span>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:35"><span class="lab"><font color="Green" title="E26">A2</font></span></a>, <a class="txt" href="#E5:35_3_2"><span class="lab"><font color="Green" title="E29">A9</font></span></a>, <a class="txt" href="#E4:35_3_2"><span class="lab"><font color="Green" title="E28">A6</font></span></a>, <a class="ref" href="ami_5.html#T26" title="AMI_5:th.26">AMI_5:26</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="35_3_3"><span class="kw">suppose </span></a><a NAME="E1:35_3_3"/>
 <a href="ami_1.html#K21" title="AMI_1:func.21">InsCode</a> <span class="p1">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  <a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p1">(<span class="default"><a href="reloc.html#K1" title="RELOC:func.1">IncAddr</a> <span class="p2">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c1">k</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c2">s</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c1">k</font></span>)</span>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Following</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p4">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Following</a> <span class="p5">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c1">k</font></span>)</span>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span><br/><div class="add"><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c5">da</font>, <font color="Maroon" title="c6">db</font> being    <a href="ami_3.html#M1" title="AMI_3:mode.1">Data-Location</a> <span class="kw"> such that </span><br/><a NAME="E3:35_3_3"/><span class="lab"><font color="Green" title="E27">A10</font></span>: 
 <a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_3.html#K4" title="AMI_3:func.4">AddTo</a> <font color="Maroon" title="c5">da</font>,<font color="Maroon" title="c6">db</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="ami_5.html#T48" title="AMI_5:th.48">AMI_5:48</a></span>;<br/><div><span class="lab"><font color="Green" title="E28">A11</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="35_3_3_1"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c7">d</font> be    <a href="ami_3.html#M1" title="AMI_3:mode.1">Data-Location</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c2">s</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c1">k</font></span>)</span>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p3">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p4">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmnorm.html#K1" title="SCMNORM:func.1">succ</a> <span class="p5">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c2">s</font></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c1">k</font></span>)</span>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Olive">b<sub>1</sub></font></span><br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="35_3_3_1_1"><span class="kw">per </span></a><a class="txt" onclick="hs(this)" href="javascript:()"><span class="kw">cases </span></a><span class="hide"><a NAME="E1:35_3_3_1_1"/>
( <font color="Maroon" title="c5">da</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">d</font> or <font color="Maroon" title="c5">da</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c7">d</font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="35_3_3_1_1_1"><span class="kw">suppose </span></a><a NAME="E1:35_3_3_1_1_1"/><span class="lab"><font color="Green" title="E29">A12</font></span>: 
<font color="Maroon" title="c5">da</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">d</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c2">s</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c1">k</font></span>)</span>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p3">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p4">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmnorm.html#K1" title="SCMNORM:func.1">succ</a> <span class="p5">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c2">s</font></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c1">k</font></span>)</span>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Olive">b<sub>1</sub></font></span><br/><div class="add"><span class="kw">hence </span><span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c2">s</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c1">k</font></span>)</span>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c7">d</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c2">s</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c1">k</font></span>)</span>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c5">da</font></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c2">s</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c1">k</font></span>)</span>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c6">db</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:35_3_3"><span class="lab"><font color="Green" title="E27">A10</font></span></a>, <a class="ref" href="ami_3.html#T9" title="AMI_3:th.9">AMI_3:9</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c5">da</font></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c2">s</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c1">k</font></span>)</span>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c6">db</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="ami_5.html#T80" title="AMI_5:th.80">AMI_5:80</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c5">da</font></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c6">db</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="ami_5.html#T80" title="AMI_5:th.80">AMI_5:80</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c7">d</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:35_3_3"><span class="lab"><font color="Green" title="E27">A10</font></span></a>, <a class="txt" href="#E1:35_3_3_1_1_1"><span class="lab"><font color="Green" title="E29">A12</font></span></a>, <a class="ref" href="ami_3.html#T9" title="AMI_3:th.9">AMI_3:9</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p3">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p4">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmnorm.html#K1" title="SCMNORM:func.1">succ</a> <span class="p5">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c2">s</font></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c1">k</font></span>)</span>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c7">d</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="ami_5.html#T80" title="AMI_5:th.80">AMI_5:80</a></span>
;<br/> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="35_3_3_1_1_2"><span class="kw">suppose </span></a><a NAME="E1:35_3_3_1_1_2"/><span class="lab"><font color="Green" title="E29">A13</font></span>: 
<font color="Maroon" title="c5">da</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c7">d</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c2">s</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c1">k</font></span>)</span>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p3">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p4">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmnorm.html#K1" title="SCMNORM:func.1">succ</a> <span class="p5">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c2">s</font></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c1">k</font></span>)</span>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Olive">b<sub>1</sub></font></span><br/><div class="add"><span class="kw">hence </span><span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c2">s</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c1">k</font></span>)</span>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c7">d</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c2">s</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c1">k</font></span>)</span>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c7">d</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:35_3_3"><span class="lab"><font color="Green" title="E27">A10</font></span></a>, <a class="ref" href="ami_3.html#T9" title="AMI_3:th.9">AMI_3:9</a></span>
<br/>.= 
<font color="Maroon" title="c2">s</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c7">d</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="ami_5.html#T80" title="AMI_5:th.80">AMI_5:80</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c7">d</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:35_3_3"><span class="lab"><font color="Green" title="E27">A10</font></span></a>, <a class="txt" href="#E1:35_3_3_1_1_2"><span class="lab"><font color="Green" title="E29">A13</font></span></a>, <a class="ref" href="ami_3.html#T9" title="AMI_3:th.9">AMI_3:9</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p3">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p4">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmnorm.html#K1" title="SCMNORM:func.1">succ</a> <span class="p5">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c2">s</font></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c1">k</font></span>)</span>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c7">d</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="ami_5.html#T80" title="AMI_5:th.80">AMI_5:80</a></span>
;<br/> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div><a NAME="E5:35_3_3"/><span class="lab"><font color="Green" title="E29">A14</font></span>: 
 <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c2">s</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c1">k</font></span>)</span>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p3">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p4">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmnorm.html#K1" title="SCMNORM:func.1">succ</a> <span class="p5">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c2">s</font></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c1">k</font></span>)</span>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:35"><span class="lab"><font color="Green" title="E25">A1</font></span></a>, <a class="txt" href="#E3:35_3_3"><span class="lab"><font color="Green" title="E27">A10</font></span></a>, <a class="ref" href="ami_3.html#T9" title="AMI_3:th.9">AMI_3:9</a></span>;<br/><a NAME="E6:35_3_3"/>
(  <a href="reloc.html#K1" title="RELOC:func.1">IncAddr</a> <span class="p1">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c1">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font> &amp;  <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmnorm.html#K1" title="SCMNORM:func.1">succ</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c2">s</font></span>)</span> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:35_3_3"><span class="lab"><font color="Green" title="E27">A10</font></span></a>, <a class="ref" href="reloc.html#T6" target="_self" title="RELOC:th.6">Th6</a>, <a class="ref" href="ami_3.html#T9" title="AMI_3:th.9">AMI_3:9</a></span>;<br/><span class="kw">hence </span><a NAME="E7:35_3_3"/>
 <a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p1">(<span class="default"><a href="reloc.html#K1" title="RELOC:func.1">IncAddr</a> <span class="p2">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c1">k</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c2">s</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c1">k</font></span>)</span>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Following</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p4">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Following</a> <span class="p5">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c1">k</font></span>)</span>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:35"><span class="lab"><font color="Green" title="E26">A2</font></span></a>, <a class="txt" href="#E5:35_3_3"><span class="lab"><font color="Green" title="E29">A14</font></span></a>, <a class="txt" href="#E4:35_3_3"><span class="lab"><font color="Green" title="E28">A11</font></span></a>, <a class="ref" href="ami_5.html#T26" title="AMI_5:th.26">AMI_5:26</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="35_3_4"><span class="kw">suppose </span></a><a NAME="E1:35_3_4"/>
 <a href="ami_1.html#K21" title="AMI_1:func.21">InsCode</a> <span class="p1">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 3
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  <a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p1">(<span class="default"><a href="reloc.html#K1" title="RELOC:func.1">IncAddr</a> <span class="p2">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c1">k</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c2">s</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c1">k</font></span>)</span>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Following</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p4">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Following</a> <span class="p5">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c1">k</font></span>)</span>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span><br/><div class="add"><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c5">da</font>, <font color="Maroon" title="c6">db</font> being    <a href="ami_3.html#M1" title="AMI_3:mode.1">Data-Location</a> <span class="kw"> such that </span><br/><a NAME="E3:35_3_4"/><span class="lab"><font color="Green" title="E27">A15</font></span>: 
 <a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_3.html#K5" title="AMI_3:func.5">SubFrom</a> <font color="Maroon" title="c5">da</font>,<font color="Maroon" title="c6">db</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="ami_5.html#T49" title="AMI_5:th.49">AMI_5:49</a></span>;<br/><div><span class="lab"><font color="Green" title="E28">A16</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="35_3_4_1"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c7">d</font> be    <a href="ami_3.html#M1" title="AMI_3:mode.1">Data-Location</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c2">s</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c1">k</font></span>)</span>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p3">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p4">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmnorm.html#K1" title="SCMNORM:func.1">succ</a> <span class="p5">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c2">s</font></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c1">k</font></span>)</span>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Olive">b<sub>1</sub></font></span><br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="35_3_4_1_1"><span class="kw">per </span></a><a class="txt" onclick="hs(this)" href="javascript:()"><span class="kw">cases </span></a><span class="hide"><a NAME="E1:35_3_4_1_1"/>
( <font color="Maroon" title="c5">da</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">d</font> or <font color="Maroon" title="c5">da</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c7">d</font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="35_3_4_1_1_1"><span class="kw">suppose </span></a><a NAME="E1:35_3_4_1_1_1"/><span class="lab"><font color="Green" title="E29">A17</font></span>: 
<font color="Maroon" title="c5">da</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">d</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c2">s</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c1">k</font></span>)</span>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p3">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p4">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmnorm.html#K1" title="SCMNORM:func.1">succ</a> <span class="p5">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c2">s</font></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c1">k</font></span>)</span>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Olive">b<sub>1</sub></font></span><br/><div class="add"><span class="kw">hence </span><span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c2">s</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c1">k</font></span>)</span>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c7">d</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c2">s</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c1">k</font></span>)</span>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c5">da</font></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c2">s</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c1">k</font></span>)</span>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c6">db</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:35_3_4"><span class="lab"><font color="Green" title="E27">A15</font></span></a>, <a class="ref" href="ami_3.html#T10" title="AMI_3:th.10">AMI_3:10</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c5">da</font></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c2">s</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c1">k</font></span>)</span>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c6">db</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="ami_5.html#T80" title="AMI_5:th.80">AMI_5:80</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c5">da</font></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c6">db</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="ami_5.html#T80" title="AMI_5:th.80">AMI_5:80</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c7">d</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:35_3_4"><span class="lab"><font color="Green" title="E27">A15</font></span></a>, <a class="txt" href="#E1:35_3_4_1_1_1"><span class="lab"><font color="Green" title="E29">A17</font></span></a>, <a class="ref" href="ami_3.html#T10" title="AMI_3:th.10">AMI_3:10</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p3">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p4">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmnorm.html#K1" title="SCMNORM:func.1">succ</a> <span class="p5">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c2">s</font></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c1">k</font></span>)</span>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c7">d</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="ami_5.html#T80" title="AMI_5:th.80">AMI_5:80</a></span>
;<br/> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="35_3_4_1_1_2"><span class="kw">suppose </span></a><a NAME="E1:35_3_4_1_1_2"/><span class="lab"><font color="Green" title="E29">A18</font></span>: 
<font color="Maroon" title="c5">da</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c7">d</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c2">s</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c1">k</font></span>)</span>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p3">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p4">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmnorm.html#K1" title="SCMNORM:func.1">succ</a> <span class="p5">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c2">s</font></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c1">k</font></span>)</span>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Olive">b<sub>1</sub></font></span><br/><div class="add"><span class="kw">hence </span><span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c2">s</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c1">k</font></span>)</span>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c7">d</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c2">s</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c1">k</font></span>)</span>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c7">d</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:35_3_4"><span class="lab"><font color="Green" title="E27">A15</font></span></a>, <a class="ref" href="ami_3.html#T10" title="AMI_3:th.10">AMI_3:10</a></span>
<br/>.= 
<font color="Maroon" title="c2">s</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c7">d</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="ami_5.html#T80" title="AMI_5:th.80">AMI_5:80</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c7">d</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:35_3_4"><span class="lab"><font color="Green" title="E27">A15</font></span></a>, <a class="txt" href="#E1:35_3_4_1_1_2"><span class="lab"><font color="Green" title="E29">A18</font></span></a>, <a class="ref" href="ami_3.html#T10" title="AMI_3:th.10">AMI_3:10</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p3">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p4">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmnorm.html#K1" title="SCMNORM:func.1">succ</a> <span class="p5">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c2">s</font></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c1">k</font></span>)</span>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c7">d</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="ami_5.html#T80" title="AMI_5:th.80">AMI_5:80</a></span>
;<br/> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div><a NAME="E5:35_3_4"/><span class="lab"><font color="Green" title="E29">A19</font></span>: 
 <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c2">s</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c1">k</font></span>)</span>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p3">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p4">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmnorm.html#K1" title="SCMNORM:func.1">succ</a> <span class="p5">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c2">s</font></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c1">k</font></span>)</span>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:35"><span class="lab"><font color="Green" title="E25">A1</font></span></a>, <a class="txt" href="#E3:35_3_4"><span class="lab"><font color="Green" title="E27">A15</font></span></a>, <a class="ref" href="ami_3.html#T10" title="AMI_3:th.10">AMI_3:10</a></span>;<br/><a NAME="E6:35_3_4"/>
(  <a href="reloc.html#K1" title="RELOC:func.1">IncAddr</a> <span class="p1">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c1">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font> &amp;  <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmnorm.html#K1" title="SCMNORM:func.1">succ</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c2">s</font></span>)</span> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:35_3_4"><span class="lab"><font color="Green" title="E27">A15</font></span></a>, <a class="ref" href="reloc.html#T7" target="_self" title="RELOC:th.7">Th7</a>, <a class="ref" href="ami_3.html#T10" title="AMI_3:th.10">AMI_3:10</a></span>;<br/><span class="kw">hence </span><a NAME="E7:35_3_4"/>
 <a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p1">(<span class="default"><a href="reloc.html#K1" title="RELOC:func.1">IncAddr</a> <span class="p2">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c1">k</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c2">s</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c1">k</font></span>)</span>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Following</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p4">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Following</a> <span class="p5">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c1">k</font></span>)</span>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:35"><span class="lab"><font color="Green" title="E26">A2</font></span></a>, <a class="txt" href="#E5:35_3_4"><span class="lab"><font color="Green" title="E29">A19</font></span></a>, <a class="txt" href="#E4:35_3_4"><span class="lab"><font color="Green" title="E28">A16</font></span></a>, <a class="ref" href="ami_5.html#T26" title="AMI_5:th.26">AMI_5:26</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="35_3_5"><span class="kw">suppose </span></a><a NAME="E1:35_3_5"/>
 <a href="ami_1.html#K21" title="AMI_1:func.21">InsCode</a> <span class="p1">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 4
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  <a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p1">(<span class="default"><a href="reloc.html#K1" title="RELOC:func.1">IncAddr</a> <span class="p2">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c1">k</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c2">s</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c1">k</font></span>)</span>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Following</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p4">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Following</a> <span class="p5">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c1">k</font></span>)</span>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span><br/><div class="add"><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c5">da</font>, <font color="Maroon" title="c6">db</font> being    <a href="ami_3.html#M1" title="AMI_3:mode.1">Data-Location</a> <span class="kw"> such that </span><br/><a NAME="E3:35_3_5"/><span class="lab"><font color="Green" title="E27">A20</font></span>: 
 <a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_3.html#K6" title="AMI_3:func.6">MultBy</a> <font color="Maroon" title="c5">da</font>,<font color="Maroon" title="c6">db</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="ami_5.html#T50" title="AMI_5:th.50">AMI_5:50</a></span>;<br/><div><span class="lab"><font color="Green" title="E28">A21</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="35_3_5_1"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c7">d</font> be    <a href="ami_3.html#M1" title="AMI_3:mode.1">Data-Location</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c2">s</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c1">k</font></span>)</span>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p3">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p4">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmnorm.html#K1" title="SCMNORM:func.1">succ</a> <span class="p5">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c2">s</font></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c1">k</font></span>)</span>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Olive">b<sub>1</sub></font></span><br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="35_3_5_1_1"><span class="kw">per </span></a><a class="txt" onclick="hs(this)" href="javascript:()"><span class="kw">cases </span></a><span class="hide"><a NAME="E1:35_3_5_1_1"/>
( <font color="Maroon" title="c5">da</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">d</font> or <font color="Maroon" title="c5">da</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c7">d</font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="35_3_5_1_1_1"><span class="kw">suppose </span></a><a NAME="E1:35_3_5_1_1_1"/><span class="lab"><font color="Green" title="E29">A22</font></span>: 
<font color="Maroon" title="c5">da</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">d</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c2">s</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c1">k</font></span>)</span>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p3">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p4">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmnorm.html#K1" title="SCMNORM:func.1">succ</a> <span class="p5">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c2">s</font></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c1">k</font></span>)</span>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Olive">b<sub>1</sub></font></span><br/><div class="add"><span class="kw">hence </span><span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c2">s</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c1">k</font></span>)</span>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c7">d</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c2">s</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c1">k</font></span>)</span>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c5">da</font></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c2">s</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c1">k</font></span>)</span>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c6">db</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:35_3_5"><span class="lab"><font color="Green" title="E27">A20</font></span></a>, <a class="ref" href="ami_3.html#T11" title="AMI_3:th.11">AMI_3:11</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c5">da</font></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c2">s</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c1">k</font></span>)</span>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c6">db</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="ami_5.html#T80" title="AMI_5:th.80">AMI_5:80</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c5">da</font></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c6">db</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="ami_5.html#T80" title="AMI_5:th.80">AMI_5:80</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c7">d</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:35_3_5"><span class="lab"><font color="Green" title="E27">A20</font></span></a>, <a class="txt" href="#E1:35_3_5_1_1_1"><span class="lab"><font color="Green" title="E29">A22</font></span></a>, <a class="ref" href="ami_3.html#T11" title="AMI_3:th.11">AMI_3:11</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p3">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p4">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmnorm.html#K1" title="SCMNORM:func.1">succ</a> <span class="p5">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c2">s</font></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c1">k</font></span>)</span>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c7">d</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="ami_5.html#T80" title="AMI_5:th.80">AMI_5:80</a></span>
;<br/> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="35_3_5_1_1_2"><span class="kw">suppose </span></a><a NAME="E1:35_3_5_1_1_2"/><span class="lab"><font color="Green" title="E29">A23</font></span>: 
<font color="Maroon" title="c5">da</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c7">d</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c2">s</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c1">k</font></span>)</span>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p3">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p4">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmnorm.html#K1" title="SCMNORM:func.1">succ</a> <span class="p5">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c2">s</font></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c1">k</font></span>)</span>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Olive">b<sub>1</sub></font></span><br/><div class="add"><span class="kw">hence </span><span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c2">s</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c1">k</font></span>)</span>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c7">d</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c2">s</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c1">k</font></span>)</span>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c7">d</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:35_3_5"><span class="lab"><font color="Green" title="E27">A20</font></span></a>, <a class="ref" href="ami_3.html#T11" title="AMI_3:th.11">AMI_3:11</a></span>
<br/>.= 
<font color="Maroon" title="c2">s</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c7">d</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="ami_5.html#T80" title="AMI_5:th.80">AMI_5:80</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c7">d</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:35_3_5"><span class="lab"><font color="Green" title="E27">A20</font></span></a>, <a class="txt" href="#E1:35_3_5_1_1_2"><span class="lab"><font color="Green" title="E29">A23</font></span></a>, <a class="ref" href="ami_3.html#T11" title="AMI_3:th.11">AMI_3:11</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p3">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p4">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmnorm.html#K1" title="SCMNORM:func.1">succ</a> <span class="p5">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c2">s</font></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c1">k</font></span>)</span>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c7">d</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="ami_5.html#T80" title="AMI_5:th.80">AMI_5:80</a></span>
;<br/> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div><a NAME="E5:35_3_5"/><span class="lab"><font color="Green" title="E29">A24</font></span>: 
 <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c2">s</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c1">k</font></span>)</span>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p3">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p4">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmnorm.html#K1" title="SCMNORM:func.1">succ</a> <span class="p5">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c2">s</font></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c1">k</font></span>)</span>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:35"><span class="lab"><font color="Green" title="E25">A1</font></span></a>, <a class="txt" href="#E3:35_3_5"><span class="lab"><font color="Green" title="E27">A20</font></span></a>, <a class="ref" href="ami_3.html#T11" title="AMI_3:th.11">AMI_3:11</a></span>;<br/><a NAME="E6:35_3_5"/>
(  <a href="reloc.html#K1" title="RELOC:func.1">IncAddr</a> <span class="p1">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c1">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font> &amp;  <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmnorm.html#K1" title="SCMNORM:func.1">succ</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c2">s</font></span>)</span> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:35_3_5"><span class="lab"><font color="Green" title="E27">A20</font></span></a>, <a class="ref" href="reloc.html#T8" target="_self" title="RELOC:th.8">Th8</a>, <a class="ref" href="ami_3.html#T11" title="AMI_3:th.11">AMI_3:11</a></span>;<br/><span class="kw">hence </span><a NAME="E7:35_3_5"/>
 <a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p1">(<span class="default"><a href="reloc.html#K1" title="RELOC:func.1">IncAddr</a> <span class="p2">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c1">k</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c2">s</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c1">k</font></span>)</span>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Following</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p4">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Following</a> <span class="p5">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c1">k</font></span>)</span>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:35"><span class="lab"><font color="Green" title="E26">A2</font></span></a>, <a class="txt" href="#E5:35_3_5"><span class="lab"><font color="Green" title="E29">A24</font></span></a>, <a class="txt" href="#E4:35_3_5"><span class="lab"><font color="Green" title="E28">A21</font></span></a>, <a class="ref" href="ami_5.html#T26" title="AMI_5:th.26">AMI_5:26</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="35_3_6"><span class="kw">suppose </span></a><a NAME="E1:35_3_6"/>
 <a href="ami_1.html#K21" title="AMI_1:func.21">InsCode</a> <span class="p1">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 5
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  <a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p1">(<span class="default"><a href="reloc.html#K1" title="RELOC:func.1">IncAddr</a> <span class="p2">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c1">k</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c2">s</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c1">k</font></span>)</span>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Following</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p4">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Following</a> <span class="p5">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c1">k</font></span>)</span>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span><br/><div class="add"><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c5">da</font>, <font color="Maroon" title="c6">db</font> being    <a href="ami_3.html#M1" title="AMI_3:mode.1">Data-Location</a> <span class="kw"> such that </span><br/><a NAME="E3:35_3_6"/><span class="lab"><font color="Green" title="E27">A25</font></span>: 
 <a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_3.html#K7" title="AMI_3:func.7">Divide</a> <font color="Maroon" title="c5">da</font>,<font color="Maroon" title="c6">db</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="ami_5.html#T51" title="AMI_5:th.51">AMI_5:51</a></span>;<br/><div><span class="lab"><font color="Green" title="E28">A26</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="35_3_6_1"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c7">d</font> be    <a href="ami_3.html#M1" title="AMI_3:mode.1">Data-Location</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c2">s</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c1">k</font></span>)</span>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p3">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p4">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmnorm.html#K1" title="SCMNORM:func.1">succ</a> <span class="p5">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c2">s</font></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c1">k</font></span>)</span>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Olive">b<sub>1</sub></font></span><br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="35_3_6_1_1"><span class="kw">per </span></a><a class="txt" onclick="hs(this)" href="javascript:()"><span class="kw">cases </span></a><span class="hide"><a NAME="E1:35_3_6_1_1"/>
( <font color="Maroon" title="c5">da</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c6">db</font> or <font color="Maroon" title="c5">da</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">db</font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="35_3_6_1_1_1"><span class="kw">suppose </span></a><a NAME="E1:35_3_6_1_1_1"/><span class="lab"><font color="Green" title="E29">A27</font></span>: 
<font color="Maroon" title="c5">da</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c6">db</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c2">s</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c1">k</font></span>)</span>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p3">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p4">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmnorm.html#K1" title="SCMNORM:func.1">succ</a> <span class="p5">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c2">s</font></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c1">k</font></span>)</span>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Olive">b<sub>1</sub></font></span><br/><div class="add"><div><span class="kw">hereby </span> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span>
<div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="35_3_6_1_1_1_1_1"><span class="kw">per </span></a><a class="txt" onclick="hs(this)" href="javascript:()"><span class="kw">cases </span></a><span class="hide"><a NAME="E1:35_3_6_1_1_1_1_1"/>
( <font color="Maroon" title="c5">da</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">d</font> or <font color="Maroon" title="c6">db</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">d</font> or ( <font color="Maroon" title="c5">da</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c7">d</font> &amp; <font color="Maroon" title="c6">db</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c7">d</font> ) )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="35_3_6_1_1_1_1_1_1"><span class="kw">suppose </span></a><a NAME="E1:35_3_6_1_1_1_1_1_1"/><span class="lab"><font color="Green" title="E30">A28</font></span>: 
<font color="Maroon" title="c5">da</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">d</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c2">s</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c1">k</font></span>)</span>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c7">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p3">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p4">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmnorm.html#K1" title="SCMNORM:func.1">succ</a> <span class="p5">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c2">s</font></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c1">k</font></span>)</span>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c7">d</font></span><br/><div class="add"><span class="kw">hence </span><span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c2">s</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c1">k</font></span>)</span>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c7">d</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c2">s</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c1">k</font></span>)</span>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c5">da</font></span>)</span> <a href="int_1.html#K5" title="INT_1:func.5">div</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c2">s</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c1">k</font></span>)</span>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c6">db</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:35_3_6"><span class="lab"><font color="Green" title="E27">A25</font></span></a>, <a class="txt" href="#E1:35_3_6_1_1_1"><span class="lab"><font color="Green" title="E29">A27</font></span></a>, <a class="ref" href="ami_3.html#T12" title="AMI_3:th.12">AMI_3:12</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c5">da</font></span>)</span> <a href="int_1.html#K5" title="INT_1:func.5">div</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c2">s</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c1">k</font></span>)</span>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c6">db</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="ami_5.html#T80" title="AMI_5:th.80">AMI_5:80</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c5">da</font></span>)</span> <a href="int_1.html#K5" title="INT_1:func.5">div</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c6">db</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="ami_5.html#T80" title="AMI_5:th.80">AMI_5:80</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c7">d</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:35_3_6"><span class="lab"><font color="Green" title="E27">A25</font></span></a>, <a class="txt" href="#E1:35_3_6_1_1_1"><span class="lab"><font color="Green" title="E29">A27</font></span></a>, <a class="txt" href="#E1:35_3_6_1_1_1_1_1_1"><span class="lab"><font color="Green" title="E30">A28</font></span></a>, <a class="ref" href="ami_3.html#T12" title="AMI_3:th.12">AMI_3:12</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p3">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p4">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmnorm.html#K1" title="SCMNORM:func.1">succ</a> <span class="p5">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c2">s</font></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c1">k</font></span>)</span>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c7">d</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="ami_5.html#T80" title="AMI_5:th.80">AMI_5:80</a></span>
;<br/> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="35_3_6_1_1_1_1_1_2"><span class="kw">suppose </span></a><a NAME="E1:35_3_6_1_1_1_1_1_2"/><span class="lab"><font color="Green" title="E30">A29</font></span>: 
<font color="Maroon" title="c6">db</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">d</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c2">s</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c1">k</font></span>)</span>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c7">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p3">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p4">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmnorm.html#K1" title="SCMNORM:func.1">succ</a> <span class="p5">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c2">s</font></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c1">k</font></span>)</span>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c7">d</font></span><br/><div class="add"><span class="kw">hence </span><span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c2">s</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c1">k</font></span>)</span>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c7">d</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c2">s</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c1">k</font></span>)</span>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c5">da</font></span>)</span> <a href="int_1.html#K6" title="INT_1:func.6">mod</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c2">s</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c1">k</font></span>)</span>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c6">db</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:35_3_6"><span class="lab"><font color="Green" title="E27">A25</font></span></a>, <a class="ref" href="ami_3.html#T12" title="AMI_3:th.12">AMI_3:12</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c5">da</font></span>)</span> <a href="int_1.html#K6" title="INT_1:func.6">mod</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c2">s</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c1">k</font></span>)</span>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c6">db</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="ami_5.html#T80" title="AMI_5:th.80">AMI_5:80</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c5">da</font></span>)</span> <a href="int_1.html#K6" title="INT_1:func.6">mod</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c6">db</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="ami_5.html#T80" title="AMI_5:th.80">AMI_5:80</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c7">d</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:35_3_6"><span class="lab"><font color="Green" title="E27">A25</font></span></a>, <a class="txt" href="#E1:35_3_6_1_1_1_1_1_2"><span class="lab"><font color="Green" title="E30">A29</font></span></a>, <a class="ref" href="ami_3.html#T12" title="AMI_3:th.12">AMI_3:12</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p3">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p4">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmnorm.html#K1" title="SCMNORM:func.1">succ</a> <span class="p5">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c2">s</font></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c1">k</font></span>)</span>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c7">d</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="ami_5.html#T80" title="AMI_5:th.80">AMI_5:80</a></span>
;<br/> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="35_3_6_1_1_1_1_1_3"><span class="kw">suppose </span></a><a NAME="E1:35_3_6_1_1_1_1_1_3"/><span class="lab"><font color="Green" title="E30">A30</font></span>: 
( <font color="Maroon" title="c5">da</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c7">d</font> &amp; <font color="Maroon" title="c6">db</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c7">d</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c2">s</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c1">k</font></span>)</span>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c7">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p3">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p4">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmnorm.html#K1" title="SCMNORM:func.1">succ</a> <span class="p5">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c2">s</font></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c1">k</font></span>)</span>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c7">d</font></span><br/><div class="add"><span class="kw">hence </span><span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c2">s</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c1">k</font></span>)</span>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c7">d</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c2">s</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c1">k</font></span>)</span>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c7">d</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:35_3_6"><span class="lab"><font color="Green" title="E27">A25</font></span></a>, <a class="ref" href="ami_3.html#T12" title="AMI_3:th.12">AMI_3:12</a></span>
<br/>.= 
<font color="Maroon" title="c2">s</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c7">d</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="ami_5.html#T80" title="AMI_5:th.80">AMI_5:80</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c7">d</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:35_3_6"><span class="lab"><font color="Green" title="E27">A25</font></span></a>, <a class="txt" href="#E1:35_3_6_1_1_1_1_1_3"><span class="lab"><font color="Green" title="E30">A30</font></span></a>, <a class="ref" href="ami_3.html#T12" title="AMI_3:th.12">AMI_3:12</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p3">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p4">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmnorm.html#K1" title="SCMNORM:func.1">succ</a> <span class="p5">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c2">s</font></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c1">k</font></span>)</span>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c7">d</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="ami_5.html#T80" title="AMI_5:th.80">AMI_5:80</a></span>
;<br/> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div></div>
<span class="kw">end;</span></div></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="35_3_6_1_1_2"><span class="kw">suppose </span></a><a NAME="E1:35_3_6_1_1_2"/><span class="lab"><font color="Green" title="E29">A31</font></span>: 
<font color="Maroon" title="c5">da</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">db</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c2">s</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c1">k</font></span>)</span>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p3">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p4">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmnorm.html#K1" title="SCMNORM:func.1">succ</a> <span class="p5">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c2">s</font></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c1">k</font></span>)</span>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Olive">b<sub>1</sub></font></span><br/><div class="add"><div><span class="kw">hereby </span> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span>
<div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="35_3_6_1_1_2_1_1"><span class="kw">per </span></a><a class="txt" onclick="hs(this)" href="javascript:()"><span class="kw">cases </span></a><span class="hide"><a NAME="E1:35_3_6_1_1_2_1_1"/>
( <font color="Maroon" title="c5">da</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">d</font> or <font color="Maroon" title="c5">da</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c7">d</font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="35_3_6_1_1_2_1_1_1"><span class="kw">suppose </span></a><a NAME="E1:35_3_6_1_1_2_1_1_1"/><span class="lab"><font color="Green" title="E30">A32</font></span>: 
<font color="Maroon" title="c5">da</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">d</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c2">s</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c1">k</font></span>)</span>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c7">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p3">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p4">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmnorm.html#K1" title="SCMNORM:func.1">succ</a> <span class="p5">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c2">s</font></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c1">k</font></span>)</span>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c7">d</font></span><br/><div class="add"><span class="kw">hence </span><span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c2">s</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c1">k</font></span>)</span>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c7">d</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c2">s</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c1">k</font></span>)</span>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c5">da</font></span>)</span> <a href="int_1.html#K6" title="INT_1:func.6">mod</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c2">s</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c1">k</font></span>)</span>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c5">da</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:35_3_6"><span class="lab"><font color="Green" title="E27">A25</font></span></a>, <a class="txt" href="#E1:35_3_6_1_1_2"><span class="lab"><font color="Green" title="E29">A31</font></span></a>, <a class="ref" href="ami_3.html#T12" title="AMI_3:th.12">AMI_3:12</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c5">da</font></span>)</span> <a href="int_1.html#K6" title="INT_1:func.6">mod</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c2">s</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c1">k</font></span>)</span>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c5">da</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="ami_5.html#T80" title="AMI_5:th.80">AMI_5:80</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c5">da</font></span>)</span> <a href="int_1.html#K6" title="INT_1:func.6">mod</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c5">da</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="ami_5.html#T80" title="AMI_5:th.80">AMI_5:80</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c7">d</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:35_3_6"><span class="lab"><font color="Green" title="E27">A25</font></span></a>, <a class="txt" href="#E1:35_3_6_1_1_2"><span class="lab"><font color="Green" title="E29">A31</font></span></a>, <a class="txt" href="#E1:35_3_6_1_1_2_1_1_1"><span class="lab"><font color="Green" title="E30">A32</font></span></a>, <a class="ref" href="ami_3.html#T12" title="AMI_3:th.12">AMI_3:12</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p3">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p4">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmnorm.html#K1" title="SCMNORM:func.1">succ</a> <span class="p5">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c2">s</font></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c1">k</font></span>)</span>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c7">d</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="ami_5.html#T80" title="AMI_5:th.80">AMI_5:80</a></span>
;<br/> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="35_3_6_1_1_2_1_1_2"><span class="kw">suppose </span></a><a NAME="E1:35_3_6_1_1_2_1_1_2"/><span class="lab"><font color="Green" title="E30">A33</font></span>: 
<font color="Maroon" title="c5">da</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c7">d</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c2">s</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c1">k</font></span>)</span>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c7">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p3">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p4">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmnorm.html#K1" title="SCMNORM:func.1">succ</a> <span class="p5">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c2">s</font></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c1">k</font></span>)</span>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c7">d</font></span><br/><div class="add"><span class="kw">hence </span><span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c2">s</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c1">k</font></span>)</span>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c7">d</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c2">s</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c1">k</font></span>)</span>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c7">d</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:35_3_6"><span class="lab"><font color="Green" title="E27">A25</font></span></a>, <a class="txt" href="#E1:35_3_6_1_1_2"><span class="lab"><font color="Green" title="E29">A31</font></span></a>, <a class="ref" href="ami_3.html#T12" title="AMI_3:th.12">AMI_3:12</a></span>
<br/>.= 
<font color="Maroon" title="c2">s</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c7">d</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="ami_5.html#T80" title="AMI_5:th.80">AMI_5:80</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c7">d</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:35_3_6"><span class="lab"><font color="Green" title="E27">A25</font></span></a>, <a class="txt" href="#E1:35_3_6_1_1_2"><span class="lab"><font color="Green" title="E29">A31</font></span></a>, <a class="txt" href="#E1:35_3_6_1_1_2_1_1_2"><span class="lab"><font color="Green" title="E30">A33</font></span></a>, <a class="ref" href="ami_3.html#T12" title="AMI_3:th.12">AMI_3:12</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p3">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p4">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmnorm.html#K1" title="SCMNORM:func.1">succ</a> <span class="p5">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c2">s</font></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c1">k</font></span>)</span>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c7">d</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="ami_5.html#T80" title="AMI_5:th.80">AMI_5:80</a></span>
;<br/> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div></div>
<span class="kw">end;</span></div></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div><a NAME="E5:35_3_6"/><span class="lab"><font color="Green" title="E29">A34</font></span>: 
 <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c2">s</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c1">k</font></span>)</span>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p3">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p4">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmnorm.html#K1" title="SCMNORM:func.1">succ</a> <span class="p5">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c2">s</font></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c1">k</font></span>)</span>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:35"><span class="lab"><font color="Green" title="E25">A1</font></span></a>, <a class="txt" href="#E3:35_3_6"><span class="lab"><font color="Green" title="E27">A25</font></span></a>, <a class="ref" href="ami_3.html#T12" title="AMI_3:th.12">AMI_3:12</a></span>;<br/><a NAME="E6:35_3_6"/>
(  <a href="reloc.html#K1" title="RELOC:func.1">IncAddr</a> <span class="p1">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c1">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font> &amp;  <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmnorm.html#K1" title="SCMNORM:func.1">succ</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c2">s</font></span>)</span> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:35_3_6"><span class="lab"><font color="Green" title="E27">A25</font></span></a>, <a class="ref" href="reloc.html#T9" target="_self" title="RELOC:th.9">Th9</a>, <a class="ref" href="ami_3.html#T12" title="AMI_3:th.12">AMI_3:12</a></span>;<br/><span class="kw">hence </span><a NAME="E7:35_3_6"/>
 <a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p1">(<span class="default"><a href="reloc.html#K1" title="RELOC:func.1">IncAddr</a> <span class="p2">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c1">k</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c2">s</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c1">k</font></span>)</span>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Following</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p4">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Following</a> <span class="p5">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c1">k</font></span>)</span>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:35"><span class="lab"><font color="Green" title="E26">A2</font></span></a>, <a class="txt" href="#E5:35_3_6"><span class="lab"><font color="Green" title="E29">A34</font></span></a>, <a class="txt" href="#E4:35_3_6"><span class="lab"><font color="Green" title="E28">A26</font></span></a>, <a class="ref" href="ami_5.html#T26" title="AMI_5:th.26">AMI_5:26</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="35_3_7"><span class="kw">suppose </span></a><a NAME="E1:35_3_7"/>
 <a href="ami_1.html#K21" title="AMI_1:func.21">InsCode</a> <span class="p1">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 6
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  <a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p1">(<span class="default"><a href="reloc.html#K1" title="RELOC:func.1">IncAddr</a> <span class="p2">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c1">k</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c2">s</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c1">k</font></span>)</span>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Following</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p4">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Following</a> <span class="p5">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c1">k</font></span>)</span>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span><br/><div class="add"><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c5">loc</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="ami_2.html#K5" title="AMI_2:func.5">NAT</a> <span class="kw"> such that </span><br/><a NAME="E3:35_3_7"/><span class="lab"><font color="Green" title="E27">A35</font></span>: 
 <a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_3.html#K8" title="AMI_3:func.8">SCM-goto</a> <font color="Maroon" title="c5">loc</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="ami_5.html#T52" title="AMI_5:th.52">AMI_5:52</a></span>;<br/><a NAME="E4:35_3_7"/><span class="lab"><font color="Green" title="E28">A36</font></span>: 
 <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">loc</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:35_3_7"><span class="lab"><font color="Green" title="E27">A35</font></span></a>, <a class="ref" href="ami_3.html#T13" title="AMI_3:th.13">AMI_3:13</a></span>;<br/><div><span class="lab"><font color="Green" title="E29">A37</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="35_3_7_1"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c6">d</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="ami_2.html#K5" title="AMI_2:func.5">NAT</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="reloc.html#K1" title="RELOC:func.1">IncAddr</a> <span class="p3">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p4">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c1">k</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c2">s</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c1">k</font></span>)</span>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K12" title="AMI_1:func.12">.</a> <font color="Maroon" title="c6">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p3">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p4">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p5">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p0">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c1">k</font></span>)</span>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span>)</span> <a href="ami_1.html#K12" title="AMI_1:func.12">.</a> <font color="Maroon" title="c6">d</font></span><br/><span class="kw">thus </span><span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="reloc.html#K1" title="RELOC:func.1">IncAddr</a> <span class="p3">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p4">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c1">k</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c2">s</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c1">k</font></span>)</span>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K12" title="AMI_1:func.12">.</a> <font color="Maroon" title="c6">d</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c2">s</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c1">k</font></span>)</span>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span>)</span> <a href="ami_1.html#K12" title="AMI_1:func.12">.</a> <font color="Maroon" title="c6">d</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="ami_1.html#D13" title="AMI_1:def.13">AMI_1:def 13</a></span>
<br/>.= 
<font color="Maroon" title="c2">s</font> <a href="ami_1.html#K12" title="AMI_1:func.12">.</a> <font color="Maroon" title="c6">d</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="ami_1.html#T112" title="AMI_1:th.112">AMI_1:112</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span> <a href="ami_1.html#K12" title="AMI_1:func.12">.</a> <font color="Maroon" title="c6">d</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="ami_1.html#D13" title="AMI_1:def.13">AMI_1:def 13</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p3">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p4">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p5">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p0">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c1">k</font></span>)</span>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span>)</span> <a href="ami_1.html#K12" title="AMI_1:func.12">.</a> <font color="Maroon" title="c6">d</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="ami_1.html#T112" title="AMI_1:th.112">AMI_1:112</a></span>
; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><a NAME="E6:35_3_7"/><span class="lab"><font color="Green" title="E30">A38</font></span>: 
 <a href="reloc.html#K1" title="RELOC:func.1">IncAddr</a> <span class="p1">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c1">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_3.html#K8" title="AMI_3:func.8">SCM-goto</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">loc</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c1">k</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:35_3_7"><span class="lab"><font color="Green" title="E27">A35</font></span></a>, <a class="ref" href="reloc.html#T10" target="_self" title="RELOC:th.10">Th10</a></span>;<br/><div><span class="lab"><font color="Green" title="E31">A39</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="35_3_7_2"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c6">d</font> be    <a href="ami_3.html#M1" title="AMI_3:mode.1">Data-Location</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="reloc.html#K1" title="RELOC:func.1">IncAddr</a> <span class="p3">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p4">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c1">k</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c2">s</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c1">k</font></span>)</span>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c6">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p3">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p4">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p5">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p0">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c1">k</font></span>)</span>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c6">d</font></span><br/><span class="kw">thus </span><span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="reloc.html#K1" title="RELOC:func.1">IncAddr</a> <span class="p3">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p4">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c1">k</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c2">s</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c1">k</font></span>)</span>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c6">d</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c2">s</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c1">k</font></span>)</span>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c6">d</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:35_3_7"><span class="lab"><font color="Green" title="E30">A38</font></span></a>, <a class="ref" href="ami_3.html#T13" title="AMI_3:th.13">AMI_3:13</a></span>
<br/>.= 
<font color="Maroon" title="c2">s</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c6">d</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="ami_5.html#T80" title="AMI_5:th.80">AMI_5:80</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c6">d</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:35_3_7"><span class="lab"><font color="Green" title="E27">A35</font></span></a>, <a class="ref" href="ami_3.html#T13" title="AMI_3:th.13">AMI_3:13</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p3">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p4">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p5">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p0">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c1">k</font></span>)</span>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c6">d</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="ami_5.html#T80" title="AMI_5:th.80">AMI_5:80</a></span>
; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div> <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="reloc.html#K1" title="RELOC:func.1">IncAddr</a> <span class="p3">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p4">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c1">k</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c2">s</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c1">k</font></span>)</span>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span>)</span></span>)</span> = 
<font color="Maroon" title="c5">loc</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c1">k</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:35_3_7"><span class="lab"><font color="Green" title="E30">A38</font></span></a>, <a class="ref" href="ami_3.html#T13" title="AMI_3:th.13">AMI_3:13</a></span>
<br/>.= 
 <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p3">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p4">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p5">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p0">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c1">k</font></span>)</span>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:35_3_7"><span class="lab"><font color="Green" title="E28">A36</font></span></a>, <a class="ref" href="funct_4.html#T121" title="FUNCT_4:th.121">FUNCT_4:121</a></span>
;<br/><span class="kw">hence </span><a NAME="E9:35_3_7"/>
 <a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p1">(<span class="default"><a href="reloc.html#K1" title="RELOC:func.1">IncAddr</a> <span class="p2">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c1">k</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c2">s</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c1">k</font></span>)</span>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Following</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p4">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Following</a> <span class="p5">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c1">k</font></span>)</span>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:35_3_7"><span class="lab"><font color="Green" title="E31">A39</font></span></a>, <a class="txt" href="#E5:35_3_7"><span class="lab"><font color="Green" title="E29">A37</font></span></a>, <a class="ref" href="ami_5.html#T26" title="AMI_5:th.26">AMI_5:26</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="35_3_8"><span class="kw">suppose </span></a><a NAME="E1:35_3_8"/>
 <a href="ami_1.html#K21" title="AMI_1:func.21">InsCode</a> <span class="p1">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 7
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  <a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p1">(<span class="default"><a href="reloc.html#K1" title="RELOC:func.1">IncAddr</a> <span class="p2">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c1">k</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c2">s</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c1">k</font></span>)</span>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Following</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p4">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Following</a> <span class="p5">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c1">k</font></span>)</span>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span><br/><div class="add"><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c5">loc</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="ami_2.html#K5" title="AMI_2:func.5">NAT</a> , <font color="Maroon" title="c6">da</font> being    <a href="ami_3.html#M1" title="AMI_3:mode.1">Data-Location</a> <span class="kw"> such that </span><br/><a NAME="E3:35_3_8"/><span class="lab"><font color="Green" title="E27">A40</font></span>: 
 <a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">da</font> <a href="ami_3.html#K9" title="AMI_3:func.9">=0_goto</a> <font color="Maroon" title="c5">loc</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="ami_5.html#T53" title="AMI_5:th.53">AMI_5:53</a></span>;<br/><a NAME="E4:35_3_8"/><span class="lab"><font color="Green" title="E28">A41</font></span>: 
 <a href="reloc.html#K1" title="RELOC:func.1">IncAddr</a> <span class="p1">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c1">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">da</font> <a href="ami_3.html#K9" title="AMI_3:func.9">=0_goto</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">loc</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c1">k</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:35_3_8"><span class="lab"><font color="Green" title="E27">A40</font></span></a>, <a class="ref" href="reloc.html#T11" target="_self" title="RELOC:th.11">Th11</a></span>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="35_3_8_1"><span class="kw">now </span></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="35_3_8_1_1"><span class="kw">per </span></a><a class="txt" onclick="hs(this)" href="javascript:()"><span class="kw">cases </span></a><span class="hide"><a NAME="E1:35_3_8_1_1"/>
( <font color="Maroon" title="c2">s</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c6">da</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  or <font color="Maroon" title="c2">s</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c6">da</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="35_3_8_1_1_1"><span class="kw">suppose </span></a><a NAME="E1:35_3_8_1_1_1"/><span class="lab"><font color="Green" title="E29">A42</font></span>: 
<font color="Maroon" title="c2">s</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c6">da</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  <a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p1">(<span class="default"><a href="reloc.html#K1" title="RELOC:func.1">IncAddr</a> <span class="p2">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c1">k</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c2">s</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c1">k</font></span>)</span>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p4">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p5">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p0">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c1">k</font></span>)</span>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span><br/><div class="add"><div><span class="lab"><font color="Green" title="E30">A43</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="35_3_8_1_1_1_1"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c7">d</font> be    <a href="ami_3.html#M1" title="AMI_3:mode.1">Data-Location</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="reloc.html#K1" title="RELOC:func.1">IncAddr</a> <span class="p3">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p4">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c1">k</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c2">s</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c1">k</font></span>)</span>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c7">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p3">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p4">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p5">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p0">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c1">k</font></span>)</span>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c7">d</font></span><br/><span class="kw">thus </span><span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="reloc.html#K1" title="RELOC:func.1">IncAddr</a> <span class="p3">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p4">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c1">k</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c2">s</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c1">k</font></span>)</span>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c7">d</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c2">s</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c1">k</font></span>)</span>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c7">d</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:35_3_8"><span class="lab"><font color="Green" title="E28">A41</font></span></a>, <a class="ref" href="ami_3.html#T14" title="AMI_3:th.14">AMI_3:14</a></span>
<br/>.= 
<font color="Maroon" title="c2">s</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c7">d</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="ami_5.html#T80" title="AMI_5:th.80">AMI_5:80</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c7">d</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:35_3_8"><span class="lab"><font color="Green" title="E27">A40</font></span></a>, <a class="ref" href="ami_3.html#T14" title="AMI_3:th.14">AMI_3:14</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p3">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p4">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p5">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p0">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c1">k</font></span>)</span>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c7">d</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="ami_5.html#T80" title="AMI_5:th.80">AMI_5:80</a></span>
; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><span class="lab"><font color="Green" title="E31">A44</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="35_3_8_1_1_1_2"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c7">d</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="ami_2.html#K5" title="AMI_2:func.5">NAT</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="reloc.html#K1" title="RELOC:func.1">IncAddr</a> <span class="p3">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p4">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c1">k</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c2">s</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c1">k</font></span>)</span>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K12" title="AMI_1:func.12">.</a> <font color="Maroon" title="c7">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p3">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p4">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p5">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p0">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c1">k</font></span>)</span>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span>)</span> <a href="ami_1.html#K12" title="AMI_1:func.12">.</a> <font color="Maroon" title="c7">d</font></span><br/><span class="kw">thus </span><span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="reloc.html#K1" title="RELOC:func.1">IncAddr</a> <span class="p3">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p4">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c1">k</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c2">s</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c1">k</font></span>)</span>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K12" title="AMI_1:func.12">.</a> <font color="Maroon" title="c7">d</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c2">s</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c1">k</font></span>)</span>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span>)</span> <a href="ami_1.html#K12" title="AMI_1:func.12">.</a> <font color="Maroon" title="c7">d</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="ami_1.html#D13" title="AMI_1:def.13">AMI_1:def 13</a></span>
<br/>.= 
<font color="Maroon" title="c2">s</font> <a href="ami_1.html#K12" title="AMI_1:func.12">.</a> <font color="Maroon" title="c7">d</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="ami_1.html#T112" title="AMI_1:th.112">AMI_1:112</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span> <a href="ami_1.html#K12" title="AMI_1:func.12">.</a> <font color="Maroon" title="c7">d</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="ami_1.html#D13" title="AMI_1:def.13">AMI_1:def 13</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p3">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p4">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p5">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p0">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c1">k</font></span>)</span>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span>)</span> <a href="ami_1.html#K12" title="AMI_1:func.12">.</a> <font color="Maroon" title="c7">d</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="ami_1.html#T112" title="AMI_1:th.112">AMI_1:112</a></span>
; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><a NAME="E4:35_3_8_1_1_1"/><span class="lab"><font color="Green" title="E32">A45</font></span>: 
 <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">loc</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:35_3_8"><span class="lab"><font color="Green" title="E27">A40</font></span></a>, <a class="txt" href="#E1:35_3_8_1_1_1"><span class="lab"><font color="Green" title="E29">A42</font></span></a>, <a class="ref" href="ami_3.html#T14" title="AMI_3:th.14">AMI_3:14</a></span>;<br/><a NAME="E5:35_3_8_1_1_1"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c2">s</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c1">k</font></span>)</span>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c6">da</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:35_3_8_1_1_1"><span class="lab"><font color="Green" title="E29">A42</font></span></a>, <a class="ref" href="ami_5.html#T80" title="AMI_5:th.80">AMI_5:80</a></span>;<br/><span class="kw">then </span> <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="reloc.html#K1" title="RELOC:func.1">IncAddr</a> <span class="p3">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p4">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c1">k</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c2">s</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c1">k</font></span>)</span>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span>)</span></span>)</span> = 
<font color="Maroon" title="c5">loc</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c1">k</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:35_3_8"><span class="lab"><font color="Green" title="E28">A41</font></span></a>, <a class="ref" href="ami_3.html#T14" title="AMI_3:th.14">AMI_3:14</a></span>
<br/>.= 
 <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p3">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p4">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p5">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p0">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c1">k</font></span>)</span>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:35_3_8_1_1_1"><span class="lab"><font color="Green" title="E32">A45</font></span></a>, <a class="ref" href="funct_4.html#T121" title="FUNCT_4:th.121">FUNCT_4:121</a></span>
;<br/><span class="kw">hence </span><a NAME="E7:35_3_8_1_1_1"/>
 <a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p1">(<span class="default"><a href="reloc.html#K1" title="RELOC:func.1">IncAddr</a> <span class="p2">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c1">k</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c2">s</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c1">k</font></span>)</span>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p4">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p5">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p0">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c1">k</font></span>)</span>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:35_3_8_1_1_1"><span class="lab"><font color="Green" title="E30">A43</font></span></a>, <a class="txt" href="#E3:35_3_8_1_1_1"><span class="lab"><font color="Green" title="E31">A44</font></span></a>, <a class="ref" href="ami_5.html#T26" title="AMI_5:th.26">AMI_5:26</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="35_3_8_1_1_2"><span class="kw">suppose </span></a><a NAME="E1:35_3_8_1_1_2"/><span class="lab"><font color="Green" title="E29">A46</font></span>: 
<font color="Maroon" title="c2">s</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c6">da</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  <a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p1">(<span class="default"><a href="reloc.html#K1" title="RELOC:func.1">IncAddr</a> <span class="p2">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c1">k</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c2">s</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c1">k</font></span>)</span>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p4">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p5">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p0">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c1">k</font></span>)</span>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span><br/><div class="add"><div><span class="lab"><font color="Green" title="E30">A47</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="35_3_8_1_1_2_1"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c7">d</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="ami_2.html#K5" title="AMI_2:func.5">NAT</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="reloc.html#K1" title="RELOC:func.1">IncAddr</a> <span class="p3">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p4">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c1">k</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c2">s</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c1">k</font></span>)</span>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K12" title="AMI_1:func.12">.</a> <font color="Maroon" title="c7">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p3">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p4">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p5">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p0">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c1">k</font></span>)</span>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span>)</span> <a href="ami_1.html#K12" title="AMI_1:func.12">.</a> <font color="Maroon" title="c7">d</font></span><br/><span class="kw">thus </span><span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="reloc.html#K1" title="RELOC:func.1">IncAddr</a> <span class="p3">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p4">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c1">k</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c2">s</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c1">k</font></span>)</span>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K12" title="AMI_1:func.12">.</a> <font color="Maroon" title="c7">d</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c2">s</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c1">k</font></span>)</span>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span>)</span> <a href="ami_1.html#K12" title="AMI_1:func.12">.</a> <font color="Maroon" title="c7">d</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="ami_1.html#D13" title="AMI_1:def.13">AMI_1:def 13</a></span>
<br/>.= 
<font color="Maroon" title="c2">s</font> <a href="ami_1.html#K12" title="AMI_1:func.12">.</a> <font color="Maroon" title="c7">d</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="ami_1.html#T112" title="AMI_1:th.112">AMI_1:112</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span> <a href="ami_1.html#K12" title="AMI_1:func.12">.</a> <font color="Maroon" title="c7">d</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="ami_1.html#D13" title="AMI_1:def.13">AMI_1:def 13</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p3">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p4">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p5">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p0">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c1">k</font></span>)</span>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span>)</span> <a href="ami_1.html#K12" title="AMI_1:func.12">.</a> <font color="Maroon" title="c7">d</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="ami_1.html#T112" title="AMI_1:th.112">AMI_1:112</a></span>
; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><span class="lab"><font color="Green" title="E31">A48</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="35_3_8_1_1_2_2"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c7">d</font> be    <a href="ami_3.html#M1" title="AMI_3:mode.1">Data-Location</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="reloc.html#K1" title="RELOC:func.1">IncAddr</a> <span class="p3">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p4">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c1">k</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c2">s</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c1">k</font></span>)</span>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c7">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p3">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p4">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p5">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p0">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c1">k</font></span>)</span>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c7">d</font></span><br/><span class="kw">thus </span><span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="reloc.html#K1" title="RELOC:func.1">IncAddr</a> <span class="p3">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p4">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c1">k</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c2">s</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c1">k</font></span>)</span>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c7">d</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c2">s</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c1">k</font></span>)</span>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c7">d</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:35_3_8"><span class="lab"><font color="Green" title="E28">A41</font></span></a>, <a class="ref" href="ami_3.html#T14" title="AMI_3:th.14">AMI_3:14</a></span>
<br/>.= 
<font color="Maroon" title="c2">s</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c7">d</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="ami_5.html#T80" title="AMI_5:th.80">AMI_5:80</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c7">d</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:35_3_8"><span class="lab"><font color="Green" title="E27">A40</font></span></a>, <a class="ref" href="ami_3.html#T14" title="AMI_3:th.14">AMI_3:14</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p3">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p4">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p5">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p0">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c1">k</font></span>)</span>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c7">d</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="ami_5.html#T80" title="AMI_5:th.80">AMI_5:80</a></span>
; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><a NAME="E4:35_3_8_1_1_2"/>
( <span class="p1">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c2">s</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c1">k</font></span>)</span>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c6">da</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  &amp;  <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmnorm.html#K1" title="SCMNORM:func.1">succ</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c2">s</font></span>)</span> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:35_3_8"><span class="lab"><font color="Green" title="E27">A40</font></span></a>, <a class="txt" href="#E1:35_3_8_1_1_2"><span class="lab"><font color="Green" title="E29">A46</font></span></a>, <a class="ref" href="ami_3.html#T14" title="AMI_3:th.14">AMI_3:14</a>, <a class="ref" href="ami_5.html#T80" title="AMI_5:th.80">AMI_5:80</a></span>;<br/><a NAME="E5:35_3_8_1_1_2"/><span class="kw">then </span>
 <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="reloc.html#K1" title="RELOC:func.1">IncAddr</a> <span class="p3">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p4">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c1">k</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c2">s</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c1">k</font></span>)</span>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p3">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p4">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p5">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p0">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c1">k</font></span>)</span>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:35"><span class="lab"><font color="Green" title="E25">A1</font></span></a>, <a class="txt" href="#E4:35_3_8"><span class="lab"><font color="Green" title="E28">A41</font></span></a>, <a class="ref" href="ami_3.html#T14" title="AMI_3:th.14">AMI_3:14</a></span>;<br/><span class="kw">hence </span><a NAME="E6:35_3_8_1_1_2"/>
 <a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p1">(<span class="default"><a href="reloc.html#K1" title="RELOC:func.1">IncAddr</a> <span class="p2">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c1">k</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c2">s</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c1">k</font></span>)</span>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p4">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p5">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p0">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c1">k</font></span>)</span>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:35_3_8_1_1_2"><span class="lab"><font color="Green" title="E31">A48</font></span></a>, <a class="txt" href="#E2:35_3_8_1_1_2"><span class="lab"><font color="Green" title="E30">A47</font></span></a>, <a class="ref" href="ami_5.html#T26" title="AMI_5:th.26">AMI_5:26</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div><span class="kw">hence </span><a NAME="E6:35_3_8"/>
 <a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p1">(<span class="default"><a href="reloc.html#K1" title="RELOC:func.1">IncAddr</a> <span class="p2">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c1">k</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c2">s</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c1">k</font></span>)</span>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Following</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p4">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Following</a> <span class="p5">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c1">k</font></span>)</span>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="35_3_9"><span class="kw">suppose </span></a><a NAME="E1:35_3_9"/>
 <a href="ami_1.html#K21" title="AMI_1:func.21">InsCode</a> <span class="p1">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 8
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  <a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p1">(<span class="default"><a href="reloc.html#K1" title="RELOC:func.1">IncAddr</a> <span class="p2">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c1">k</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c2">s</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c1">k</font></span>)</span>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Following</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p4">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Following</a> <span class="p5">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c1">k</font></span>)</span>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span><br/><div class="add"><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c5">loc</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="ami_2.html#K5" title="AMI_2:func.5">NAT</a> , <font color="Maroon" title="c6">da</font> being    <a href="ami_3.html#M1" title="AMI_3:mode.1">Data-Location</a> <span class="kw"> such that </span><br/><a NAME="E3:35_3_9"/><span class="lab"><font color="Green" title="E27">A49</font></span>: 
 <a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">da</font> <a href="ami_3.html#K10" title="AMI_3:func.10">&gt;0_goto</a> <font color="Maroon" title="c5">loc</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="ami_5.html#T54" title="AMI_5:th.54">AMI_5:54</a></span>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="35_3_9_1"><span class="kw">now </span></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="35_3_9_1_1"><span class="kw">per </span></a><a class="txt" onclick="hs(this)" href="javascript:()"><span class="kw">cases </span></a><span class="hide"><a NAME="E1:35_3_9_1_1"/>
( <font color="Maroon" title="c2">s</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c6">da</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  or <font color="Maroon" title="c2">s</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c6">da</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="35_3_9_1_1_1"><span class="kw">suppose </span></a><a NAME="E1:35_3_9_1_1_1"/><span class="lab"><font color="Green" title="E28">A50</font></span>: 
<font color="Maroon" title="c2">s</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c6">da</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  <a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">da</font> <a href="ami_3.html#K10" title="AMI_3:func.10">&gt;0_goto</a> <span class="p2">(<span class="default"><font color="Maroon" title="c5">loc</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c1">k</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c2">s</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c1">k</font></span>)</span>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p4">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p5">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p0">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c1">k</font></span>)</span>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span><br/><div class="add"><div><span class="lab"><font color="Green" title="E29">A51</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="35_3_9_1_1_1_1"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c7">d</font> be    <a href="ami_3.html#M1" title="AMI_3:mode.1">Data-Location</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">da</font> <a href="ami_3.html#K10" title="AMI_3:func.10">&gt;0_goto</a> <span class="p3">(<span class="default"><font color="Maroon" title="c5">loc</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c1">k</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c2">s</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c1">k</font></span>)</span>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c7">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p3">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p4">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p5">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p0">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c1">k</font></span>)</span>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c7">d</font></span><br/><span class="kw">thus </span><span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">da</font> <a href="ami_3.html#K10" title="AMI_3:func.10">&gt;0_goto</a> <span class="p3">(<span class="default"><font color="Maroon" title="c5">loc</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c1">k</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c2">s</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c1">k</font></span>)</span>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c7">d</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c2">s</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c1">k</font></span>)</span>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c7">d</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="ami_3.html#T15" title="AMI_3:th.15">AMI_3:15</a></span>
<br/>.= 
<font color="Maroon" title="c2">s</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c7">d</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="ami_5.html#T80" title="AMI_5:th.80">AMI_5:80</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c7">d</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:35_3_9"><span class="lab"><font color="Green" title="E27">A49</font></span></a>, <a class="ref" href="ami_3.html#T15" title="AMI_3:th.15">AMI_3:15</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p3">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p4">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p5">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p0">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c1">k</font></span>)</span>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c7">d</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="ami_5.html#T80" title="AMI_5:th.80">AMI_5:80</a></span>
; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><span class="lab"><font color="Green" title="E30">A52</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="35_3_9_1_1_1_2"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c7">d</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="ami_2.html#K5" title="AMI_2:func.5">NAT</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">da</font> <a href="ami_3.html#K10" title="AMI_3:func.10">&gt;0_goto</a> <span class="p3">(<span class="default"><font color="Maroon" title="c5">loc</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c1">k</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c2">s</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c1">k</font></span>)</span>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K12" title="AMI_1:func.12">.</a> <font color="Maroon" title="c7">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p3">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p4">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p5">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p0">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c1">k</font></span>)</span>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span>)</span> <a href="ami_1.html#K12" title="AMI_1:func.12">.</a> <font color="Maroon" title="c7">d</font></span><br/><span class="kw">thus </span><span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">da</font> <a href="ami_3.html#K10" title="AMI_3:func.10">&gt;0_goto</a> <span class="p3">(<span class="default"><font color="Maroon" title="c5">loc</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c1">k</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c2">s</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c1">k</font></span>)</span>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K12" title="AMI_1:func.12">.</a> <font color="Maroon" title="c7">d</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c2">s</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c1">k</font></span>)</span>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span>)</span> <a href="ami_1.html#K12" title="AMI_1:func.12">.</a> <font color="Maroon" title="c7">d</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="ami_1.html#D13" title="AMI_1:def.13">AMI_1:def 13</a></span>
<br/>.= 
<font color="Maroon" title="c2">s</font> <a href="ami_1.html#K12" title="AMI_1:func.12">.</a> <font color="Maroon" title="c7">d</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="ami_1.html#T112" title="AMI_1:th.112">AMI_1:112</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span> <a href="ami_1.html#K12" title="AMI_1:func.12">.</a> <font color="Maroon" title="c7">d</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="ami_1.html#D13" title="AMI_1:def.13">AMI_1:def 13</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p3">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p4">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p5">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p0">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c1">k</font></span>)</span>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span>)</span> <a href="ami_1.html#K12" title="AMI_1:func.12">.</a> <font color="Maroon" title="c7">d</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="ami_1.html#T112" title="AMI_1:th.112">AMI_1:112</a></span>
; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><a NAME="E4:35_3_9_1_1_1"/><span class="lab"><font color="Green" title="E31">A53</font></span>: 
 <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">loc</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:35_3_9"><span class="lab"><font color="Green" title="E27">A49</font></span></a>, <a class="txt" href="#E1:35_3_9_1_1_1"><span class="lab"><font color="Green" title="E28">A50</font></span></a>, <a class="ref" href="ami_3.html#T15" title="AMI_3:th.15">AMI_3:15</a></span>;<br/><a NAME="E5:35_3_9_1_1_1"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c2">s</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c1">k</font></span>)</span>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c6">da</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:35_3_9_1_1_1"><span class="lab"><font color="Green" title="E28">A50</font></span></a>, <a class="ref" href="ami_5.html#T80" title="AMI_5:th.80">AMI_5:80</a></span>;<br/><span class="kw">then </span> <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">da</font> <a href="ami_3.html#K10" title="AMI_3:func.10">&gt;0_goto</a> <span class="p3">(<span class="default"><font color="Maroon" title="c5">loc</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c1">k</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c2">s</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c1">k</font></span>)</span>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span>)</span></span>)</span> = 
<font color="Maroon" title="c5">loc</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c1">k</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="ami_3.html#T15" title="AMI_3:th.15">AMI_3:15</a></span>
<br/>.= 
 <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p3">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p4">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p5">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p0">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c1">k</font></span>)</span>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:35_3_9_1_1_1"><span class="lab"><font color="Green" title="E31">A53</font></span></a>, <a class="ref" href="funct_4.html#T121" title="FUNCT_4:th.121">FUNCT_4:121</a></span>
;<br/><span class="kw">hence </span><a NAME="E7:35_3_9_1_1_1"/>
 <a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">da</font> <a href="ami_3.html#K10" title="AMI_3:func.10">&gt;0_goto</a> <span class="p2">(<span class="default"><font color="Maroon" title="c5">loc</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c1">k</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c2">s</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c1">k</font></span>)</span>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p4">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p5">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p0">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c1">k</font></span>)</span>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:35_3_9_1_1_1"><span class="lab"><font color="Green" title="E29">A51</font></span></a>, <a class="txt" href="#E3:35_3_9_1_1_1"><span class="lab"><font color="Green" title="E30">A52</font></span></a>, <a class="ref" href="ami_5.html#T26" title="AMI_5:th.26">AMI_5:26</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="35_3_9_1_1_2"><span class="kw">suppose </span></a><a NAME="E1:35_3_9_1_1_2"/><span class="lab"><font color="Green" title="E28">A54</font></span>: 
<font color="Maroon" title="c2">s</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c6">da</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  <a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">da</font> <a href="ami_3.html#K10" title="AMI_3:func.10">&gt;0_goto</a> <span class="p2">(<span class="default"><font color="Maroon" title="c5">loc</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c1">k</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c2">s</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c1">k</font></span>)</span>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p4">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p5">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p0">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c1">k</font></span>)</span>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span><br/><div class="add"><div><span class="lab"><font color="Green" title="E29">A55</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="35_3_9_1_1_2_1"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c7">d</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="ami_2.html#K5" title="AMI_2:func.5">NAT</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">da</font> <a href="ami_3.html#K10" title="AMI_3:func.10">&gt;0_goto</a> <span class="p3">(<span class="default"><font color="Maroon" title="c5">loc</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c1">k</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c2">s</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c1">k</font></span>)</span>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K12" title="AMI_1:func.12">.</a> <font color="Maroon" title="c7">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p3">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p4">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p5">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p0">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c1">k</font></span>)</span>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span>)</span> <a href="ami_1.html#K12" title="AMI_1:func.12">.</a> <font color="Maroon" title="c7">d</font></span><br/><span class="kw">thus </span><span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">da</font> <a href="ami_3.html#K10" title="AMI_3:func.10">&gt;0_goto</a> <span class="p3">(<span class="default"><font color="Maroon" title="c5">loc</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c1">k</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c2">s</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c1">k</font></span>)</span>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K12" title="AMI_1:func.12">.</a> <font color="Maroon" title="c7">d</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c2">s</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c1">k</font></span>)</span>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span>)</span> <a href="ami_1.html#K12" title="AMI_1:func.12">.</a> <font color="Maroon" title="c7">d</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="ami_1.html#D13" title="AMI_1:def.13">AMI_1:def 13</a></span>
<br/>.= 
<font color="Maroon" title="c2">s</font> <a href="ami_1.html#K12" title="AMI_1:func.12">.</a> <font color="Maroon" title="c7">d</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="ami_1.html#T112" title="AMI_1:th.112">AMI_1:112</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span> <a href="ami_1.html#K12" title="AMI_1:func.12">.</a> <font color="Maroon" title="c7">d</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="ami_1.html#D13" title="AMI_1:def.13">AMI_1:def 13</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p3">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p4">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p5">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p0">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c1">k</font></span>)</span>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span>)</span> <a href="ami_1.html#K12" title="AMI_1:func.12">.</a> <font color="Maroon" title="c7">d</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="ami_1.html#T112" title="AMI_1:th.112">AMI_1:112</a></span>
; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><span class="lab"><font color="Green" title="E30">A56</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="35_3_9_1_1_2_2"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c7">d</font> be    <a href="ami_3.html#M1" title="AMI_3:mode.1">Data-Location</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">da</font> <a href="ami_3.html#K10" title="AMI_3:func.10">&gt;0_goto</a> <span class="p3">(<span class="default"><font color="Maroon" title="c5">loc</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c1">k</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c2">s</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c1">k</font></span>)</span>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c7">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p3">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p4">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p5">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p0">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c1">k</font></span>)</span>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c7">d</font></span><br/><span class="kw">thus </span><span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">da</font> <a href="ami_3.html#K10" title="AMI_3:func.10">&gt;0_goto</a> <span class="p3">(<span class="default"><font color="Maroon" title="c5">loc</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c1">k</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c2">s</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c1">k</font></span>)</span>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c7">d</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c2">s</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c1">k</font></span>)</span>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c7">d</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="ami_3.html#T15" title="AMI_3:th.15">AMI_3:15</a></span>
<br/>.= 
<font color="Maroon" title="c2">s</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c7">d</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="ami_5.html#T80" title="AMI_5:th.80">AMI_5:80</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c7">d</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:35_3_9"><span class="lab"><font color="Green" title="E27">A49</font></span></a>, <a class="ref" href="ami_3.html#T15" title="AMI_3:th.15">AMI_3:15</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p3">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p4">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p5">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p0">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c1">k</font></span>)</span>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c7">d</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="ami_5.html#T80" title="AMI_5:th.80">AMI_5:80</a></span>
; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><a NAME="E4:35_3_9_1_1_2"/>
( <span class="p1">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c2">s</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c1">k</font></span>)</span>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c6">da</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  &amp;  <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmnorm.html#K1" title="SCMNORM:func.1">succ</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c2">s</font></span>)</span> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:35_3_9"><span class="lab"><font color="Green" title="E27">A49</font></span></a>, <a class="txt" href="#E1:35_3_9_1_1_2"><span class="lab"><font color="Green" title="E28">A54</font></span></a>, <a class="ref" href="ami_3.html#T15" title="AMI_3:th.15">AMI_3:15</a>, <a class="ref" href="ami_5.html#T80" title="AMI_5:th.80">AMI_5:80</a></span>;<br/><a NAME="E5:35_3_9_1_1_2"/><span class="kw">then </span>
 <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">da</font> <a href="ami_3.html#K10" title="AMI_3:func.10">&gt;0_goto</a> <span class="p3">(<span class="default"><font color="Maroon" title="c5">loc</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c1">k</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c2">s</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c1">k</font></span>)</span>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p3">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p4">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p5">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p0">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c1">k</font></span>)</span>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:35"><span class="lab"><font color="Green" title="E25">A1</font></span></a>, <a class="ref" href="ami_3.html#T15" title="AMI_3:th.15">AMI_3:15</a></span>;<br/><span class="kw">hence </span><a NAME="E6:35_3_9_1_1_2"/>
 <a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">da</font> <a href="ami_3.html#K10" title="AMI_3:func.10">&gt;0_goto</a> <span class="p2">(<span class="default"><font color="Maroon" title="c5">loc</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c1">k</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c2">s</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c1">k</font></span>)</span>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p4">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p5">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p0">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c1">k</font></span>)</span>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:35_3_9_1_1_2"><span class="lab"><font color="Green" title="E30">A56</font></span></a>, <a class="txt" href="#E2:35_3_9_1_1_2"><span class="lab"><font color="Green" title="E29">A55</font></span></a>, <a class="ref" href="ami_5.html#T26" title="AMI_5:th.26">AMI_5:26</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div><span class="kw">hence </span><a NAME="E5:35_3_9"/>
 <a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p1">(<span class="default"><a href="reloc.html#K1" title="RELOC:func.1">IncAddr</a> <span class="p2">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c1">k</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c2">s</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c1">k</font></span>)</span>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Following</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p4">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Following</a> <span class="p5">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c1">k</font></span>)</span>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:35_3_9"><span class="lab"><font color="Green" title="E27">A49</font></span></a>, <a class="ref" href="reloc.html#T12" target="_self" title="RELOC:th.12">Th12</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div>

</div>
